Numerical solution of linear and nonlinear Fredholm integral equations by using weighted mean-value theorem

Mean value theorems for both derivatives and integrals are very useful tools in mathematics. They can be used to obtain very important inequalities and to prove basic theorems of mathematical analysis. In this article, a semi-analytical method that is based on weighted mean-value theorem for obtaini...

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Detalles Bibliográficos
Autor principal: Altürk, Ahmet
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2016
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5108753/
https://www.ncbi.nlm.nih.gov/pubmed/27933241
http://dx.doi.org/10.1186/s40064-016-3645-8
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author Altürk, Ahmet
author_facet Altürk, Ahmet
author_sort Altürk, Ahmet
collection PubMed
description Mean value theorems for both derivatives and integrals are very useful tools in mathematics. They can be used to obtain very important inequalities and to prove basic theorems of mathematical analysis. In this article, a semi-analytical method that is based on weighted mean-value theorem for obtaining solutions for a wide class of Fredholm integral equations of the second kind is introduced. Illustrative examples are provided to show the significant advantage of the proposed method over some existing techniques.
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spelling pubmed-51087532016-12-08 Numerical solution of linear and nonlinear Fredholm integral equations by using weighted mean-value theorem Altürk, Ahmet Springerplus Research Mean value theorems for both derivatives and integrals are very useful tools in mathematics. They can be used to obtain very important inequalities and to prove basic theorems of mathematical analysis. In this article, a semi-analytical method that is based on weighted mean-value theorem for obtaining solutions for a wide class of Fredholm integral equations of the second kind is introduced. Illustrative examples are provided to show the significant advantage of the proposed method over some existing techniques. Springer International Publishing 2016-11-14 /pmc/articles/PMC5108753/ /pubmed/27933241 http://dx.doi.org/10.1186/s40064-016-3645-8 Text en © The Author(s) 2016 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Altürk, Ahmet
Numerical solution of linear and nonlinear Fredholm integral equations by using weighted mean-value theorem
title Numerical solution of linear and nonlinear Fredholm integral equations by using weighted mean-value theorem
title_full Numerical solution of linear and nonlinear Fredholm integral equations by using weighted mean-value theorem
title_fullStr Numerical solution of linear and nonlinear Fredholm integral equations by using weighted mean-value theorem
title_full_unstemmed Numerical solution of linear and nonlinear Fredholm integral equations by using weighted mean-value theorem
title_short Numerical solution of linear and nonlinear Fredholm integral equations by using weighted mean-value theorem
title_sort numerical solution of linear and nonlinear fredholm integral equations by using weighted mean-value theorem
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5108753/
https://www.ncbi.nlm.nih.gov/pubmed/27933241
http://dx.doi.org/10.1186/s40064-016-3645-8
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